A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto a target portion of the substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In that instance, a patterning device, which is alternatively referred to as a mask or a reticle, may be used to generate a circuit pattern to be formed on an individual layer of the IC. This pattern can be transferred onto a target portion (e.g., comprising part of, one, or several dies) on a substrate (e.g., a silicon wafer). Transfer of the pattern is typically via imaging onto a layer of radiation-sensitive material (resist) provided on the substrate. In general, a single substrate will contain a network of adjacent target portions that are successively patterned. Known lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing an entire pattern onto the target portion at one time, and so-called scanners, in which each target portion is irradiated by scanning the pattern through a radiation beam in a given direction (the “scanning”-direction) while synchronously scanning the substrate parallel or anti parallel to this direction. It is also possible to transfer the pattern from the patterning device to the substrate by imprinting the pattern onto the substrate.
In order to allow for a number of patterned layers to be positioned on the substrate, it is desirable to accurately set the position of the substrate relative to the radiation beam and the patterning device. This may be performed by accurately positioning the substrate on a substrate table and positioning the substrate table relative to the radiation beam and the patterning device.
Alignment of a substrate may be performed by an alignment system. For example, a number of alignment marks on the substrate are measured to derive a co-ordinate system, which is compared to a modeled grid to derive the positions of features on the substrate. However, clamping of the substrate on the substrate table, or wafer distortion occurring in non-lithography process steps, may cause distortion of the substrate, which can be monitored by comparison of the measurements to the grid. Models describing the wafer grid may be created, which are used in exposing wafers so as to compensate for the distortions.
Measurements of the overlay, which is the alignment of successive layers formed on the substrate, may also be made using a modeled grid. The modeled grid can be used to describe the overlay error over the substrate with respect to the previous layer, and may be produced and used in a control loop to ensure lot-to-lot consistency. It has been found that overlay can be improved by using a non-linear grid instead of a linear grid within the model. However, small changes in the shape of a non-linear grid can have dramatic effects on the individual comparisons of the measurements and the model. Thus monitoring of the individual fit parameters is meaningless and “run-to-run” control rules, such as parameter damping are not helpful.